Mechanisms, Upscaling, and Prediction of Anomalous Dispersion in Heterogeneous Porous Media

Abstract

We study the upscaling and prediction of large‐scale solute dispersion in heterogeneous porous media with focus on preasymptotic or anomalous features such as tailing in breakthrough curves and spatial concentration profiles as well as nonlinear evolution of the spatial variance of the concentration distribution. Spatial heterogeneity in the hydraulic medium properties is represented in a stochastic modeling approach. Direct numerical Monte Carlo simulations of flow and advective particle motion combined with a Markov model for streamwise particle velocities give insight in the mechanisms of preasymptotic and asymptotic solute transport in terms of the statistical signatures of the medium and flow heterogeneity. Based on the representation of equidistantly sampled particle velocities as a Markov process, we derive an upscaled continuous time random walk approach that can be conditioned on the flow velocities and thus hydraulic conductivity in the injection region. In this modeling framework, we identify the Eulerian velocity distribution, advective tortuosity, and the correlation length of particle velocities as the key quantities for large‐scale transport prediction. Thus, the upscaled model predicts the spatial concentration profiles, their first and second centered moments, and the breakthrough curves obtained from direct numerical Monte Carlo simulations in spatially heterogeneous conductivity fields. The presented approach allows to relate the medium and flow properties to large‐scale preasymptotic and asymptotic solute dispersion.

Anomalous Transport in Three‐Dimensional Discrete Fracture Networks: Interplay Between Aperture Heterogeneity and Injection Modes

“…The convergence toward a steady‐state velocity PDF shows the ergodic property of the underlying flow field. Note that ergodicity can be recovered even in purely advective flows as particles sample heterogeneous velocities along the trajectories in ergodic velocity fields (Comolli et al., 2019; Puyguiraud et al., 2019).…”

New Simplified Models of Single‐Well Push‐Pull Tests With Mixing Effect

“…Some of these assumptions may be relaxed in future studies to deal with realistic, heterogeneous formation with an autocorrelated permeability field. For that purpose, other approaches such as stochastic modeling and/or numerical modeling, rather than the deterministic analytical modeling of this study, are probably more suitable (Comolli et al, 2019; Di Dato et al, 2019; Fiori et al, 2017).…”

Transport Upscaling in Highly Heterogeneous Aquifers and the Prediction of Tracer Dispersion at the MADE Site

“…Thus, advective particle motion is quantified by the following stochastic evolution equations for the longitudinal particle position x(s) and the advective travel time t a (s) (Dentz et al, 2016;Comolli et al, 2019):…”

“…The distance s along the streamline is in general larger than the linear travel distance x in the mean flow direction. They are projected onto each other through the advective tortuosity χ , which is given by the ratio of the average flow speed ⟨ q ⟩ and the average velocity component ⟨ q 1 ⟩ in mean flow direction, (Comolli et al., 2019). The angular brackets denote suitably chosen averages, here spatial and ensemble average.…”

“…In this paper, we address the questions of upscaling and prediction of dispersion in highly heterogeneous aquifers in terms of medium and flow heterogeneity using transport‐independent parameters. We use a stochastic TDRW approach (Comolli et al., 2019; Hakoun et al., 2019) that accounts for heterogeneous advection. This approach propagates particles in space and time according to a velocity Markov model that is determined by the distribution of the Eulerian flow speed and correlation length.…”